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362.75, 395.77, 422.1, 437.41], "y_lo": [268.84, 310.17, 346.75, 371.77, 386.1, 387.41]}], "rationale": "Inverse-cube central attraction mu/r^3. e01 r=150 v=80 circular gives mu=(r v)^2=1.44e8. e04 r=200 v=69: h^2>mu, k=0.494, r=r0/cos(k theta) predicts r=216.8 at 46deg, observed 217.3. e05 r=120 v=80: h^2<mu kappa=0.75 predicts crash to 38px at 140.6deg, observed 38.4px. Confirms 1/r^3 vs 1/r^2. Test predictions from analytic 1/r^3 solution: super-critical u=A cos(k theta-delta), t=(tan(k theta-delta)+tan delta)/(h A^2 k); sub-critical u=u0 cosh(kappa theta)+B sinh, integrated numerically.", "self_confidence": 0.85}, "tests": ["media/test0.mp4", "media/test1.mp4"], "probe_times": [0.5, 1.2, 1.9, 2.5667, 3.2667, 3.9667], "grade": {"error": 0.003828046886894979, "pass": true, "coverage": 1.0}, "truth": {"form": "power", "constants": {"alpha": 3.0108346533866834, "k": 151943195.96819392}}, "ledger_entries": 16, "ledger_ok": true, "cost_usd": 0.0274}, "p1": {"calibration": [{"d": 8, "n50": 19.097557411312756, "ci": [18.744147558903773, 19.44219340819109], "width": 2.107757458414424, "trials": 80}, {"d": 10, "n50": 27.831685620666065, "ci": [27.339729277255348, 28.33250773715487], "width": 2.47238405223642, "trials": 80}, {"d": 12, "n50": 38.793089556053665, "ci": [38.23589131776829, 39.422639169960064], "width": 3.2019391252011196, "trials": 80}, {"d": 14, "n50": 52.243743531889194, "ci": [51.4688007953165, 52.995177006535144], "width": 3.6563992556811793, "trials": 80}, {"d": 16, "n50": 66.51965663653867, "ci": [65.45550211633596, 67.47718732765865], "width": 4.403360604841242, "trials": 80}, {"d": 18, "n50": 83.26915788069226, "ci": [82.04803872321177, 84.43632553337221], "width": 4.2356067113059925, "trials": 80}, {"d": 20, "n50": 103.40412105187905, "ci": [102.15138683959893, 104.99576958191273], "width": 5.240623280763488, "trials": 80}, {"d": 22, "n50": 123.11193639861712, "ci": [121.62152411751043, 124.66329609210315], "width": 5.670293063869183, "trials": 80}, {"d": 24, "n50": 148.0805319468339, "ci": [146.26800169827433, 149.80435602074246], "width": 5.29170633074985, "trials": 80}], "target": [{"d": 30, "n50": 227.53971518152863, "ci": [224.88851715602192, 229.8332851515163], "width": 6.400548453753967, "trials": 80}, {"d": 36, "n50": 326.1274727366212, "ci": [322.9940058282849, 329.4123134718401], "width": 8.172573775602226, "trials": 80}, {"d": 44, "n50": 489.97911104902175, "ci": [484.5453848738972, 493.9959541852659], "width": 10.392584354326088, "trials": 80}], "sealed_sha256": "eeb1185a15e319548730b459adfb8109083fed1508bb2122cf25a3f0b9e8d196", "grade": {"w0_from_calibration": 0.26117137540579854, "table": {"asymptotic_step": {"30": {"pred_n50": 225.0, "meas_n50": 227.53971518152863, "n50_inside_95ci": true, "pred_width": null, "meas_width": 6.400548453753967, "brier": 0.033035714285714286}, "36": {"pred_n50": 324.0, "meas_n50": 326.1274727366212, "n50_inside_95ci": true, "pred_width": null, "meas_width": 8.172573775602226, "brier": 0.026785714285714284}, "44": {"pred_n50": 484.0, "meas_n50": 489.97911104902175, "n50_inside_95ci": false, "pred_width": null, "meas_width": 10.392584354326088, "brier": 0.02321428571428571}}, "statistical_dimension": {"30": {"pred_n50": 232.5, "meas_n50": 227.53971518152863, "n50_inside_95ci": false, "pred_width": 7.8351412621739565, "meas_width": 6.400548453753967, "brier": 0.027863654452467034}, "36": {"pred_n50": 333.0, "meas_n50": 326.1274727366212, "n50_inside_95ci": false, "pred_width": 9.402169514608747, "meas_width": 8.172573775602226, "brier": 0.024657560967013877}, "44": {"pred_n50": 495.0, "meas_n50": 489.97911104902175, "n50_inside_95ci": false, "pred_width": 11.491540517855135, "meas_width": 10.392584354326088, "brier": 0.019802764096522218}}, "finite_size_fit": {"30": {"pred_n50": 228.16362380463264, "meas_n50": 227.53971518152863, "n50_inside_95ci": true, "pred_width": 7.2197602413397775, "meas_width": 6.400548453753967, "brier": 0.025575029517793835}, "36": {"pred_n50": 327.26463019545224, "meas_n50": 326.1274727366212, "n50_inside_95ci": true, "pred_width": 8.541741210840293, "meas_width": 8.172573775602226, "brier": 0.02203933644553704}, "44": {"pred_n50": 487.3993053832117, "meas_n50": 489.97911104902175, "n50_inside_95ci": true, "pred_width": 10.278251990785245, "meas_width": 10.392584354326088, "brier": 0.01903235571841368}}, "muse_spark": {"30": {"pred_n50": 227.9, "meas_n50": 227.53971518152863, "n50_inside_95ci": true, "pred_width": 7.18, "meas_width": 6.400548453753967, "brier": 0.025553159283763283}, "36": {"pred_n50": 326.9, "meas_n50": 326.1274727366212, "n50_inside_95ci": true, "pred_width": 8.53, "meas_width": 8.172573775602226, "brier": 0.021997820713720525}, "44": {"pred_n50": 486.9, "meas_n50": 489.97911104902175, "n50_inside_95ci": true, "pred_width": 10.33, "meas_width": 10.392584354326088, "brier": 0.01907664401787443}}}, "statistical_dimension_sealed_before_targets": true}, "spark": "n50(d) = d^2/4 + 2.9; 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